In 2010, Bristol Palin and Johnston agreed Bristol would have primary physical custody and the two would share legal custody, subject to Bristol's resolution if they couldn't agree.

Bristol Palin and Tripp appeared on the recent Lifetime series "Bristol Palin: Life's a Tripp," in which Johnston's presence in his son's life, or lack thereof, was part of the story line. The website TMZ reported last month that Johnston wanted full custody.

An attorney for Bristol Palin didn't immediately respond to a request for comment.